Deriving the time-dependent dyadic Green’s functions in conductive anisotropic media

Abstract

A homogeneous anisotropic conductive medium, characterized by symmetric positive definite permeability and conductivity tensors, is considered in the paper. In this anisotropic medium, the electric and magnetic dyadic Green’s functions are defined as electric and magnetic fields arising from impulsive current dipoles and satisfying the time-dependent Maxwell’s equations in quasi-static approximation. A new method of deriving these dyadic Green’s functions is suggested in the paper. This method consists of several steps: equations for electric and magnetic dyadic Green’s functions are written in terms of the Fourier images; explicit formulae for the Fourier images of dyadic Green’s functions are derived using the matrix transformations and solutions of some ordinary differential equations depending on the Fourier parameters; the inverse Fourier transform is applied numerically to obtained formulae to find dyadic Green’s functions values. Using suggested method images of electric and magnetic dyadic Green’s function components are obtained in such conductive anisotropic medium as the white matter of a human brain.